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Simplifying 2 = -12x2 + 360x Reorder the terms: 2 = 360x + -12x2 Solving 2 = 360x + -12x2 Solving for variable 'x'. Reorder the terms: 2 + -360x + 12x2 = 360x + -360x + -12x2 + 12x2 Combine like terms: 360x + -360x = 0 2 + -360x + 12x2 = 0 + -12x2 + 12x2 2 + -360x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 2 + -360x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -180x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -180x + 6x2)' equal to zero and attempt to solve: Simplifying 1 + -180x + 6x2 = 0 Solving 1 + -180x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -30x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -30x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -30x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -30x + x2 = 0 + -0.1666666667 -30x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -30x + x2 = -0.1666666667 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -0.1666666667 + 225 Reorder the terms: 225 + -30x + x2 = -0.1666666667 + 225 Combine like terms: -0.1666666667 + 225 = 224.8333333333 225 + -30x + x2 = 224.8333333333 Factor a perfect square on the left side: (x + -15)(x + -15) = 224.8333333333 Calculate the square root of the right side: 14.994443415 Break this problem into two subproblems by setting (x + -15) equal to 14.994443415 and -14.994443415.Subproblem 1
x + -15 = 14.994443415 Simplifying x + -15 = 14.994443415 Reorder the terms: -15 + x = 14.994443415 Solving -15 + x = 14.994443415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 14.994443415 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.994443415 + 15 x = 14.994443415 + 15 Combine like terms: 14.994443415 + 15 = 29.994443415 x = 29.994443415 Simplifying x = 29.994443415Subproblem 2
x + -15 = -14.994443415 Simplifying x + -15 = -14.994443415 Reorder the terms: -15 + x = -14.994443415 Solving -15 + x = -14.994443415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -14.994443415 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.994443415 + 15 x = -14.994443415 + 15 Combine like terms: -14.994443415 + 15 = 0.005556585 x = 0.005556585 Simplifying x = 0.005556585Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.994443415, 0.005556585}Solution
x = {29.994443415, 0.005556585}
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